This is the html-rendered R markdown file (Rmd) which accompanies the manuscript:
Huber-Huber, C. & Melcher, D. (2020) The behavioural preview effect with faces results from predictive processing across the saccade. Manuscript submitted for publication.

The code used to generate this file reproduces all statistics and figures in the manuscript from the data which is provided as well. For all background information information about the study, however, please refer to the manuscript file.

Figure and table numbers correspond to figures and tables in the manuscript.

1 Overview of the data

1.1 Proportion correct

Here, we check the average performance across the experiment in the tilt discrimination task. Participants with less than 60% correct responses are excluded assuming that they did not do the task.

    partnr Training prop.corr prop.corr<0.60
 1:     33  Invalid 0.5191364           TRUE
 2:     37  Invalid 0.5322266           TRUE
 3:      8  Invalid 0.5430528           TRUE
 4:     34    Valid 0.5475709           TRUE
 5:     27  Invalid 0.5616438           TRUE
 6:     40    Valid 0.5714286           TRUE
 7:     18  Invalid 0.6050831          FALSE
 8:     12  Invalid 0.6113744          FALSE
 9:     19    Valid 0.6174168          FALSE
10:     36    Valid 0.6656863          FALSE
11:     25  Invalid 0.7247796          FALSE
12:     38    Valid 0.7431641          FALSE
13:     29  Invalid 0.7446184          FALSE
14:     22  Invalid 0.7497556          FALSE
15:     16  Invalid 0.7526882          FALSE
16:     15    Valid 0.7563601          FALSE
17:     32  Invalid 0.7608696          FALSE
18:     11    Valid 0.7617647          FALSE
19:      5    Valid 0.7626953          FALSE
20:      3  Invalid 0.7689282          FALSE
21:     17    Valid 0.7763672          FALSE
22:      2    Valid 0.7778865          FALSE
23:      6  Invalid 0.7864838          FALSE
24:     26    Valid 0.8164062          FALSE
25:     39  Invalid 0.8189824          FALSE
26:      9    Valid 0.8258317          FALSE
27:     24  Invalid 0.8406647          FALSE
28:     10  Invalid 0.8437500          FALSE
29:      7    Valid 0.8447266          FALSE
30:     13    Valid 0.8476562          FALSE
31:     28    Valid 0.8554688          FALSE
32:     35  Invalid 0.8563050          FALSE
33:     20  Invalid 0.8631476          FALSE
34:     21    Valid 0.8875855          FALSE
35:     31  Invalid 0.8895406          FALSE
36:     23    Valid 0.8935547          FALSE
37:      4  Invalid 0.8955665          FALSE
38:     41  Invalid 0.8970588          FALSE
39:     14  Invalid 0.9111328          FALSE
40:     30    Valid 0.9149560          FALSE
41:      1    Valid 0.9274510          FALSE
    partnr Training prop.corr prop.corr<0.60

Thus, participants excluded are: 33, 37, 8, 34, 27, 40.

Number of participants per training group:

Training
  Valid Invalid 
     17      18

1.2 Demographics

Age:

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   18.0    20.0    21.0    22.5    24.0    41.0

Gender (0 -> female; 1 -> male):

gender
 0  1 
25 10

Handedness (0 -> left; 1 -> right):

handedness
 0  1 
 6 29

Eyedness (0 -> left; 1 -> right):

eyedness
 0  1 
14 21

2 Response time

For details on the model fitting and model comparison approach, see the corresponding Rmd source code file.

2.1 Model comparisons

Supplementary Table S1. Response time model comparisons to determine the random effects structure. Each column presents the parameters (random and fixed) of a model. Models in adjacent columns are compared to each other by likelihood ratios tests. Test results (χ2, degress of freedom, and p value) for a model pair are printed for the right model of each pair in the last three rows. Observations - the number of single trials for the model; AICc - Akaike’s Information Criterion corrected for small sample sizes; Df - model degrees of freedom; χ2 - statistic for the likelihood ratio test, for each model the difference in deviance compared to the model to the left; χ2 Df - degrees of freedom for the likelihood ratio test, for each model the difference in Df compared to the model to the left; p - the p-value for the likelihood ratio test.
Dependent variable:
-1 / Response time [sec]
Fitting method:
REML REML REML REML
(1) (2) (3) (4)
Random effects variances
Participant
(Intercept) 0.039 0.049 0.049 0.049
Target Orientation (In-Up) 0.002 0.002 0.002
Preview (Inv-Val) 0.001 0.001 0.001
Trial number 0.010 0.010 0.010
Target Orientation x Preview 0.003 0.003 0.003
Target Orientation x Trial number 0.0001 0.0001 0.0001
Preview x Trial number 0 0
Target Orientation x Preview x Trial number 0
Residual Variance 0.039 0.036 0.036 0.036
Fixed effects
Target Orientation (In-Up) 0.033 0.037 0.037 0.037
(0.007) (0.010) (0.010) (0.010)
t = 4.675 t = 3.749 t = 3.749 t = 3.749
Preview (Inv-Val) 0.044 0.041 0.041 0.041
(0.007) (0.009) (0.009) (0.009)
t = 6.143 t = 4.549 t = 4.549 t = 4.549
Training (Inv-Val) -0.144 -0.138 -0.138 -0.138
(0.068) (0.075) (0.075) (0.075)
t = -2.128 t = -1.831 t = -1.831 t = -1.831
Trial number -0.074 -0.077 -0.077 -0.077
(0.004) (0.017) (0.017) (0.017)
t = -20.736 t = -4.388 t = -4.388 t = -4.388
Target Orientation x Preview -0.010 -0.014 -0.014 -0.014
(0.014) (0.016) (0.016) (0.016)
t = -0.729 t = -0.841 t = -0.841 t = -0.841
Target Orientation x Training 0.010 0.002 0.002 0.002
(0.014) (0.020) (0.020) (0.020)
t = 0.696 t = 0.083 t = 0.083 t = 0.083
Preview x Training -0.074 -0.070 -0.070 -0.070
(0.014) (0.018) (0.018) (0.018)
t = -5.242 t = -3.848 t = -3.848 t = -3.848
Target Orientation x Trial number 0.016 0.013 0.013 0.013
(0.007) (0.007) (0.007) (0.007)
t = 2.269 t = 1.866 t = 1.866 t = 1.866
Preview x Trial number 0.001 0.003 0.003 0.003
(0.007) (0.007) (0.007) (0.007)
t = 0.079 t = 0.425 t = 0.425 t = 0.425
Training x Trial number 0.065 0.058 0.058 0.058
(0.007) (0.035) (0.035) (0.035)
t = 9.151 t = 1.676 t = 1.676 t = 1.676
Target Orientation x Preview x Training 0.015 0.010 0.010 0.010
(0.028) (0.033) (0.033) (0.033)
t = 0.522 t = 0.300 t = 0.300 t = 0.300
Target Orientation x Preview x Trial number 0.007 0.012 0.012 0.012
(0.014) (0.014) (0.014) (0.014)
t = 0.486 t = 0.854 t = 0.854 t = 0.854
Target Orientation x Training x Trial number -0.007 -0.002 -0.002 -0.002
(0.014) (0.014) (0.014) (0.014)
t = -0.469 t = -0.122 t = -0.122 t = -0.122
Preview x Training x Trial number 0.033 0.028 0.028 0.028
(0.014) (0.014) (0.014) (0.014)
t = 2.359 t = 2.051 t = 2.051 t = 2.051
Target Orientation x Preview x Training x Trial number -0.015 -0.017 -0.017 -0.017
(0.028) (0.027) (0.027) (0.027)
t = -0.541 t = -0.618 t = -0.618 t = -0.618
Grand mean -1.025 -1.022 -1.022 -1.022
(0.034) (0.038) (0.038) (0.038)
t = -30.344 t = -27.213 t = -27.213 t = -27.213
Observations 12,671 12,671 12,671 12,671
AICc -4852.342 -5702.931 -5700.924 -5698.916
Log Likelihood 2444.198 2874.509 2874.509 2874.509
Deviance -4888.396 -5749.019 -5749.019 -5749.019
Df 18 23 24 25
χ2 860.623 0 0
χ2 Df 5 1 1
p < .001 1.000 1.000
Model is singular † †

The table of model comparisons above indicates that the model with the complete random effects structure is singular. Removing the random slope of the highest-order interaction with zero variance, still leads to a singular model. Removing the next zero variance component leads to a model that we call the maximum identifiable model (here Model 2). This model is better than the model without random slopes as can be seen from the model comparison indices in that table.

2.2 Results from the maximum identified model

Figure 2. Estimated marginal means from the maximum identified model on response time data (Model 2). The preview effect, the difference between valid and invalid preview trials, depended on the training condition. In contrast to valid training, there was no evidence for a preview effect with invalid training (see also Models 2a and 2b below). Note that effect estimates were obtained for the first trial of the test phase. Error bars represent asymptotic confidence intervals.

Figure 2. Estimated marginal means from the maximum identified model on response time data (Model 2). The preview effect, the difference between valid and invalid preview trials, depended on the training condition. In contrast to valid training, there was no evidence for a preview effect with invalid training (see also Models 2a and 2b below). Note that effect estimates were obtained for the first trial of the test phase. Error bars represent asymptotic confidence intervals.

Figure 3. Fixed effect coefficients of the maximum identified linear mixed model on response times (Model 2).

Figure 3. Fixed effect coefficients of the maximum identified linear mixed model on response times (Model 2).

Fixed effects of Model 2. Estimate, standard error, t-value, and lower/upper limit of 95% profile confidence intervals. This table contains the data plotted in Figure 3.
Parameter Estimate Std. Error t value 2.5 % 97.5 %
((Intercept)) -1.022 0.038 -27.213 -1.095 -0.948
Target Orientation (In-Up) 0.037 0.010 3.749 0.018 0.056
Preview (Inv-Val) 0.041 0.009 4.549 0.024 0.059
Training (Inv-Val) -0.138 0.075 -1.831 -0.285 0.009
Trial number -0.077 0.017 -4.388 -0.111 -0.042
Target Orientation x Preview -0.014 0.016 -0.841 -0.046 0.018
Target Orientation x Training 0.002 0.020 0.083 -0.037 0.040
Preview x Training -0.070 0.018 -3.848 -0.105 -0.034
Target Orientation x Trial number 0.013 0.007 1.866 -0.001 0.027
Preview x Trial number 0.003 0.007 0.425 -0.010 0.016
Training x Trial number 0.058 0.035 1.676 -0.010 0.127
Target Orientation x Preview x Training 0.010 0.033 0.300 -0.054 0.074
Target Orientation x Preview x Trial number 0.012 0.014 0.854 -0.015 0.038
Target Orientation x Training x Trial number -0.002 0.014 -0.122 -0.029 0.026
Preview x Training x Trial number 0.028 0.014 2.051 0.001 0.055
Target Orientation x Preview x Training x Trial number -0.017 0.027 -0.618 -0.070 0.037
Figure 4. Response times showed an interaction of Training x Preview x Trial Number, which suggested that training with only valid trials resulted in a larger preview effect than training with only invalid trials particularly in the beginning of the test phase. The preview effect then evolved in opposite directions for both training groups. Compared to the invalid training group, the preview effect in the valid training group declined. Each dot is one trial. Trial number was standardized and centered on the first trial of the test phase.

Figure 4. Response times showed an interaction of Training x Preview x Trial Number, which suggested that training with only valid trials resulted in a larger preview effect than training with only invalid trials particularly in the beginning of the test phase. The preview effect then evolved in opposite directions for both training groups. Compared to the invalid training group, the preview effect in the valid training group declined. Each dot is one trial. Trial number was standardized and centered on the first trial of the test phase.

Note, Figure 4 is zoomed-in at the y-axis. Only half of all individual trial data points (sampled randomly) are plotted in order to decrease the size of the plot.

2.3 Valid and invalid training groups analysed separately

Here we follow up the interaction Preview x Training x Trial Number to see whether the preview effects are significant within the training groups.

Supplementary Table S2. Fixed effects of Model 2a, the maximum identified model on response times of the valid training group. Estimate, standard error, t-value, and lower/upper limit of 95% profile confidence intervals.
Parameter Estimate Std. Error t value 2.5 % 97.5 %
((Intercept)) -0.953 0.056 -17.112 -1.065 -0.841
Target Orientation (In-Up) 0.036 0.013 2.799 0.011 0.061
Preview (Inv-Val) 0.076 0.015 5.154 0.047 0.105
Trial number -0.106 0.030 -3.525 -0.166 -0.045
Target Orientation x Preview -0.019 0.024 -0.800 -0.067 0.028
Target Orientation x Trial number 0.014 0.009 1.524 -0.004 0.032
Preview x Trial number -0.011 0.009 -1.187 -0.029 0.007
Target Orientation x Preview x Trial number 0.021 0.019 1.124 -0.016 0.057
Supplementary Table S3. Fixed effects of Model 2b, the maximum identified model on response times of the invalid training group. Estimate, standard error, t-value, and lower/upper limit of 95% profile confidence intervals.
Parameter Estimate Std. Error t value 2.5 % 97.5 %
((Intercept)) -1.091 0.051 -21.520 -1.193 -0.989
Target Orientation (In-Up) 0.038 0.015 2.563 0.009 0.067
Preview (Inv-Val) 0.007 0.011 0.607 -0.015 0.028
Trial number -0.047 0.019 -2.535 -0.084 -0.010
Target Orientation x Preview -0.007 0.022 -0.316 -0.051 0.036
Target Orientation x Trial number 0.012 0.011 1.053 -0.011 0.034
Preview x Trial number 0.017 0.010 1.676 -0.003 0.036
Target Orientation x Preview x Trial number 0.002 0.020 0.118 -0.037 0.041

2.4 Response times summary

The Preview x Training x Trial Number interaction is significant. Note that in the figure illustrating this interaction, the preview effect is the difference between dashed (invalid preview) and solid (valid preview) lines in the direction of the y-axis. If the training phase was valid, there is a preview effect in the beginning of the following test phase which decreases in the course of the test phase. If training phase was invalid, there is a smaller/no preview effect in the beginning of the following test phase which then, compared to the valid training condition, tends to increase. In other words, the influence of training equals across time.

Besides this interaction, there is a significant main effect of Target Orientation. This effect is in the expected direction known from previous research, i.e. faster responses with upright than with inverted targets. The direction of the effect can be seen from the contrasts of the Target Orientation factor and the value of the effect estimate. The contrast is In-Up, meaning inverted minus upright. That means the effect estimate is calculated by subtracing upright target trials from inverted target trials. That means positive values indicate larger dependent variable values for inverted than for upright targets. The dependent variable transformation of -1 / RT before model fitting ensured that larger values still mean slower responses (i.e. maintain the direction of the effect). Thus, given a positive value for the Target Orientation effect estimate () and confidence intervals excluding zero, we can conclude that responses were significanly faster with upright than with inverted targets.

3 Error rate / proportion correct

For details on the model fitting and model comparison approach, see the corresponding Rmd source code file.

3.1 Model comparisons

Supplementary Table S4. Error rate model comparisons to determine the random effects structure. Each column presents the parameters (random and fixed) of a model. Models in adjacent columns are compared to each other by likelihood ratios tests. Test results (χ2, degress of freedom, and p value) for a model pair are printed for the right model of each pair in the last three rows. Observations - the number of single trials for the model; AICc - Akaike’s Information Criterion corrected for small sample sizes; Df - model degrees of freedom; χ2 - statistic for the likelihood ratio test, for each model the difference in deviance compared to the model to the left; χ2 Df - degrees of freedom for the likelihood ratio test, for each model the difference in Df compared to the model to the left; p - the p-value for the likelihood ratio test.
Dependent variable:
Task error (log odds)
(5) (6) (7) (8)
Random effects variances
Participant
(Intercept) 0.344 0.340 0.340 0.340
Target Orientation (In-Up) 0.134 0.134 0.134
Preview (Inv-Val) 0.027 0.027 0.027
Trial number 0.032 0.032 0.032
Target Orientation x Trial number 0.043 0.043 0.043
Target Orientation x Preview x Trial number 0.136 0.136 0.136
Preview x Trial number 0 0
Target Orientation x Preview 0
Residual Variance 1 1 1 1
Fixed effects
Target Orientation (In-Up) 0.655 0.676 0.676 0.676
(0.085) (0.107) (0.107) (0.107)
t = 7.725 t = 6.331 t = 6.331 t = 6.331
Preview (Inv-Val) -0.107 -0.101 -0.101 -0.101
(0.085) (0.090) (0.090) (0.090)
t = -1.265 t = -1.125 t = -1.125 t = -1.125
Training (Inv-Val) 0.082 0.070 0.070 0.070
(0.216) (0.216) (0.216) (0.216)
t = 0.381 t = 0.326 t = 0.326 t = 0.326
Trial number 0.020 -0.003 -0.003 -0.003
(0.042) (0.054) (0.054) (0.054)
t = 0.463 t = -0.048 t = -0.048 t = -0.048
Target Orientation x Preview 0.028 0.027 0.027 0.027
(0.169) (0.170) (0.170) (0.170)
t = 0.166 t = 0.158 t = 0.158 t = 0.158
Target Orientation x Training -0.045 -0.009 -0.009 -0.009
(0.170) (0.213) (0.213) (0.213)
t = -0.265 t = -0.043 t = -0.043 t = -0.043
Preview x Training -0.156 -0.160 -0.160 -0.160
(0.169) (0.179) (0.179) (0.179)
t = -0.921 t = -0.892 t = -0.892 t = -0.892
Target Orientation x Trial number -0.199 -0.177 -0.177 -0.177
(0.084) (0.093) (0.093) (0.093)
t = -2.363 t = -1.893 t = -1.893 t = -1.893
Preview x Trial number -0.023 -0.031 -0.031 -0.031
(0.084) (0.085) (0.085) (0.085)
t = -0.267 t = -0.370 t = -0.370 t = -0.370
Training x Trial number -0.115 -0.111 -0.111 -0.111
(0.084) (0.106) (0.106) (0.106)
t = -1.363 t = -1.053 t = -1.053 t = -1.053
Target Orientation x Preview x Training -0.071 -0.068 -0.068 -0.068
(0.339) (0.340) (0.340) (0.340)
t = -0.210 t = -0.200 t = -0.200 t = -0.200
Target Orientation x Preview x Trial number -0.057 -0.071 -0.071 -0.071
(0.169) (0.182) (0.182) (0.182)
t = -0.338 t = -0.391 t = -0.391 t = -0.391
Target Orientation x Training x Trial number 0.006 0.033 0.033 0.033
(0.169) (0.186) (0.186) (0.186)
t = 0.034 t = 0.178 t = 0.178 t = 0.178
Preview x Training x Trial number 0.027 0.022 0.022 0.022
(0.169) (0.170) (0.170) (0.170)
t = 0.160 t = 0.127 t = 0.127 t = 0.127
Target Orientation x Preview x Training x Trial number 0.088 0.105 0.105 0.105
(0.337) (0.363) (0.363) (0.363)
t = 0.261 t = 0.288 t = 0.288 t = 0.288
Grand mean -1.538 -1.543 -1.543 -1.543
(0.108) (0.108) (0.108) (0.108)
t = -14.216 t = -14.257 t = -14.257 t = -14.257
Observations 15,765 15,765 15,765 15,765
AICc 14817.779 14775.659 14777.665 14779.671
Log Likelihood -7391.87 -7365.797 -7365.797 -7365.797
Deviance 14783.741 14731.595 14731.595 14731.595
Df 17 22 23 24
χ2 52.146 0 0
χ2 Df 5 1 1
p < .001 1.000 1.000
Model is singular † †

The table of model comparisons above indicates that the model with the complete random effects structure is singular. Removing the random slope of the less interesting component with zero variance, still leads to a singular model. Removing the next zero variance component leads to the maximum identifiable model (Model 6). This model is better than the model without random slopes as can be seen from the model comparison indices in the table above.

3.2 Results from the maximum identified model

Figure 5. Fixed effect coefficients of the maximum identified generalized linear model on task errors (Model 6).

Figure 5. Fixed effect coefficients of the maximum identified generalized linear model on task errors (Model 6).

Fixed effects of Model 6. Estimate and lower/upper limit of 95% profile confidence intervals. This table contains the data plotted in Figure 5.
Parameter Estimate 2.5 % 97.5 %
((Intercept)) -1.543 -1.762 -1.328
Target Orientation (In-Up) 0.676 0.467 0.890
Preview (Inv-Val) -0.101 -0.278 0.076
Training (Inv-Val) 0.070 -0.363 0.503
Trial number -0.003 -0.114 0.102
Target Orientation x Preview 0.027 -0.307 0.361
Target Orientation x Training -0.009 -0.429 0.416
Preview x Training -0.160 -0.513 0.193
Target Orientation x Trial number -0.177 -0.359 0.012
Preview x Trial number -0.031 -0.198 0.135
Training x Trial number -0.111 -0.325 0.102
Target Orientation x Preview x Training -0.068 -0.735 0.599
Target Orientation x Preview x Trial number -0.071 -0.431 0.285
Target Orientation x Training x Trial number 0.033 -0.331 0.405
Preview x Training x Trial number 0.022 -0.312 0.355
Target Orientation x Preview x Training x Trial number 0.105 -0.610 0.820
Additional figure illustrating the Target Orientation x Trial Number interaction which is strictly speaking not significant and anyway theoretically not relevant.

Additional figure illustrating the Target Orientation x Trial Number interaction which is strictly speaking not significant and anyway theoretically not relevant.

3.3 Error rates summary

Clearly less task error with upright than with inverted targets. In addition, there is a borderline significant Target Orientation x Trial Number interaction in the direction of a decreasing target orientation effect (inverted minus upright) across the test phase. However, strickly speaking, this effect is not significant and it is theoretically not relevant, so we do not interpret it and do not mention it in the paper.

4 Results summary

Training influenced the preview effect in response times. In the beginning of the test phase, there was a clear preview effect if participants had trained with only valid trials. However, after invalid training there was no evidence for a preview effect. Moreover, this change in the preview effect equalled during the test phase.

In addition but theoretically not relevant, target face orientation, affected performance leading to slower responses and more errors when target faces were inverted compared to when they were upright.

5 Session information

R version 3.6.1 (2019-07-05)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Sierra 10.12.6

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib

locale:
[1] C

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] knitr_1.24        citr_0.3.2        stargazer_5.2.2   boot_1.3-23       emmeans_1.4.5     lme4_1.1-21       Matrix_1.2-17     ggplot2_3.2.1    
[9] data.table_1.12.2

loaded via a namespace (and not attached):
 [1] gtools_3.8.1     tidyselect_0.2.5 xfun_0.9         reshape2_1.4.3   purrr_0.3.2      splines_3.6.1    lattice_0.20-38  colorspace_1.4-1
 [9] miniUI_0.1.1.1   htmltools_0.3.6  yaml_2.2.0       rlang_0.4.0      pillar_1.4.2     nloptr_1.2.1     later_0.8.0      glue_1.3.1      
[17] withr_2.1.2      plyr_1.8.4       stringr_1.4.0    munsell_0.5.0    gtable_0.3.0     mvtnorm_1.0-11   coda_0.19-3      evaluate_0.14   
[25] labeling_0.3     httpuv_1.5.1     highr_0.8        Rcpp_1.0.2       xtable_1.8-4     scales_1.0.0     promises_1.0.1   mime_0.7        
[33] digest_0.6.20    stringi_1.4.3    dplyr_0.8.3      shiny_1.3.2      grid_3.6.1       tools_3.6.1      magrittr_1.5     lazyeval_0.2.2  
[41] tibble_2.1.3     crayon_1.3.4     pkgconfig_2.0.2  MASS_7.3-51.4    estimability_1.3 assertthat_0.2.1 minqa_1.2.4      rmarkdown_1.15  
[49] rstudioapi_0.10  R6_2.4.0         nlme_3.1-140     compiler_3.6.1